In that case I suspect a logic in the "suspicious" code's test. In other words it sees no changes for a long time, then tries to check for change, thinks it sees one, and returns a few lines, waits more and repeats.

Almost certainly a bug, report it to the module author and/or try to debug yourself. (Putting a debug statement in File::Tail to test when it enters that code will verify my guess, though it won't fix it.)